Microdomain theories

Floudas and coworkers [88] investigated the static and kinetic aspects of the order-disorder transition in SI2 and SIB miktoarm stars using SAXS and rheology. At temperatures above the order-disorder transition (ODT) the mean field theory describes the experimental results quite well. Near the ODT, SAXS profiles gave evidence for the existence of fluctuations. Both samples separated into cylindrical microdomains below the ODT. The ODT was determined on shear oriented samples and found, by SAXS, to be 379 K in both cases. This was confirmed by rheology. The discontinuities in SAXS peak intensity and in the storage modulus near the ODT were more pronounced for the miktoarm stars than for the diblocks. The %N values, where % is the interaction parameter and N the... 

In this paper, a molecular thermodynamic approach is developed to predict the structural and compositional characteristics of microemulsions. The theory can be applied not only to oil-in-water and water-in-cil droplet-type microemulsions but also to bicontinuous microemulsions. This treatment constitutes an extension of our earlier approaches to micelles, mixed micelles, and solubilization but also takes into account the self-association of alcohol in the oil phase and the excluded-volume interactions among the droplets. Illustrative results are presented for an anionic surfactant (SDS) pentanol cyclohexane water NaCl system. Microstructur al features including the droplet radius, the thickness of the surfactant layer at the interface, the number of molecules of various species in a droplet, the size and composition dispersions of the droplets, and the distribution of the surfactant, oil, alcohol, and water molecules in the various microdomains are calculated. Further, the model allows the identification of the transition from a two-phase droplet-type microemulsion system to a three-phase microemulsion system involving a bicontinuous microemulsion. The persistence length of the bicontinuous microemulsion is also predicted by the model. Finally, the model permits the calculation of the interfacial tension between a microemulsion and the coexisting phase. 

Helfand E (1975) Block copolymer theory. HI. Statistical mechanics of the microdomain structure. Macromolecules 8 552-556... 

Helfand has presented a general theory of inhomogeneous polymeric systems and has applied it to the interface between immiscible honmpolymers and to block copolymers In order to simplify the problem of the numerical calculation of the microdomain sizes, he has derived from his general theory a narrow interface approximation The values predicted by the simplified theory for the dimensions of the lamellar block copolymer microdomains are in good agreement with the experimental results ... 

As discussed below, the quality of the alignment (and even its direction in the case of lamellar morphology), is influenced by temperature, as well as the frequency and strain amplitude of the aligning shear field. No general theory for the alignment of block-copolymer phases has yet been developed. However, studies of a number of different block-copolymer systems show that in ordered states with cylindrical domains, shear orients the cylinders parallel to the flow, while for lamallar microdomains, two different shear-induced orientations are commonly found, depending on alignment conditions in both of these orientations, the flow direction lies in the plane of the lamellae. 

Rod—coil block copolymers have both rigid rod and block copolymer characteristics. The formation of liquid crystalline nematic phase is characteristic of rigid rod, and the formation of various nanosized structures is a block copolymer characteristic. A theory for the nematic ordering of rigid rods in a solution has been initiated by Onsager and Flory,28-29 and the fundamentals of liquid crystals have been reviewed in books.30 31 The theoretical study of coil-coil block copolymer was initiated by Meier,32 and the various geometries of microdomains and micro phase transitions are now fully understood. A phase diagram for a structurally symmetric coil—coil block copolymer has been theoretically predicted as a... 

Their Tammann temperatures are low. As a consequence, these lattices are in a metastable state, near these temperatures. If two structures are closely related, as we shall see in the next section, the two solids will be able to form either coherent interfaces or solid solutions. In these cases, "hybrid crystals, in which microdomains of both phases coexist, can be formed according to UBBELOHDE s theory (43), which considers strain energy E and internal surface energy ri (44). The free enthalpy of a domain (1) in a matrix of structure (2) is given by ... 

LC-BCPs provide theorists with novel model systems for developing new theories of polymer behavior [41]. Consider the process of microphase separation in LC-BCPs starting from the disordered BCP structure (or isotropic solution) (Scheme 1). As the temperature decreases, the system will undergo microphase separation to form ordered microdomain structures. As temperature falls past the LC clearing transition temperature (Jj) the LC block will shift from the isotropic phase to a LC phase. If this temperature is lower than the Tg of the other... 

In 2005, Tyler et al. were the first to predict the existence of the orthorhombic Fddd as an equilibrium structure in the phase diagram of diblock copolymers. Using self-consistent field theory, the calculated phase diagram is shown in Fig. 4.3a [13, 16]. Two years later, Takenaka et al. were the first to deliver the experimental proof for the existence of the Fddd microdomain structure, discovered in a PS-ft-PI diblock copolymer melt [17], Thereafter, Kim et al. determined the Fddd phase boundaries in PS- -PI melts, as illustrated in Fig.4.3b [14, 18]. Although it was believed that the latest phase diagram of diblock copolymer was complete. Ho et al. in 2009 reported the discovery of a helical cylinder phase in poly(styrene)-f>-poly (L-lactic acid) melts, see Fig.4.3c [15]. 

Microdomain stmctures of 3-miktoarm star terpolymers in a three-dimensional space were investigated using the dynamic density functional theory (DDFT). Analysis of DDFT demonstrates that the junction points are restricted to lie on... 

In pRISM theory, the MIST process is directly reflected in the normalized static structure factor, S(copolymer system is cooled and microdomains are forming, the peak scattering intensity grows in a mean-field maimer corresponding to the linear portion of the S(< ) curve in the coordinates Extrapolation of this linear portion to divergent intensity defines an apparent mean-field spinodal temperature. ... 

The microphase separation of block copolymers is sometimes called order-disorder transition (ODT). The self-consistent-field theory (SCFT) provides a mean-field method to calculate various geometric shapes of microdomains. Edwards first introduced the SCFT into polymer systems on the basis of making path integrals along chain conformations (Edwards 1965). Helfand applied it to the mean-field description of immiscible polymer blends on the basis of the Gaussian-chain model... 

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